The adjoint of the matrix [tex]\left[\begin{array}{cc}1&0\\2&-1\end{array}\right][/tex] is [tex]\left[\begin{array}{cc}-1&0\\-2&1\end{array}\right][/tex]
How to determine the adjoint?The matrix is given as:
[tex]\left[\begin{array}{cc}1&0\\2&-1\end{array}\right][/tex]
For a matrix A be represented as:
[tex]A = \left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex]
The adjoint is:
[tex]Adj = \left[\begin{array}{cc}d&-b\\-c&a\end{array}\right][/tex]
Using the above format, we have:
[tex]Adj = \left[\begin{array}{cc}-1&0\\-2&1\end{array}\right][/tex]
Hence, the adjoint of the matrix [tex]\left[\begin{array}{cc}1&0\\2&-1\end{array}\right][/tex] is [tex]\left[\begin{array}{cc}-1&0\\-2&1\end{array}\right][/tex]
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cos(x)= square root of 3 over 2
The measure of angle x is 30°
How to find the measure of angle x?Trigonometry is the branch of mathematics that deals with the relationships between the sides and angles of triangles, particularly right triangles. It is concerned with the measurement of angles and the calculation of sines, cosines, and tangents of those angles.
These ratios are known as trigonometric functions and they are used to relate the ratios of the sides of a right triangle to the angles opposite or adjacent to the right angle.
cos(x) = (√3)/2
x = cos⁻¹((√3)/2) = 30°
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Students in jakes class were numbered in order from 1 to 24 jake was asked to choose classmates numbered with multiples of 5 to be in his group which number could be the number of a classmate in his group
Answer:
the possible classmates numbered with multiples of 5 that Jake can choose are 5,10,15,20.
Step-by-step explanation:
Multiples of 5 are numbers that are obtained by multiplying 5 by any whole number. So, to find the classmates numbered with multiples of 5, we can start by multiplying 5 by 1, then by 2, 3, and so on. The first few multiples of 5 are 5, 10, 15, 20, 25 and so on. Since the students are numbered from 1 to 24, only students whose numbers are less than or equal to 24 can be chosen.
So the possible classmates numbered with multiples of 5 that Jake can choose are 5,10,15,20.
Which rule represents the relationship in the table above?
Oy=x
Oy = 2.54x
Oy=x+1.54
Oy=x²
The rule that is used for the relationship in the table is
B. y = 2.54xHow to find the rule as used for the tableThe relationship between x in inches and y in centimeters as represented can be solved by directly on the table or using the knowledge of conversion of inches to centimeter
Another procedure to solve this is to try the equations as in the options;
The first option is y = x, this is obviously wrong as the values in the y and the values in the x are not equal.
The second option, is y = 2.54x
for x = 1, y = 2.54 * 1 = 1
for x = 2, y = 2.54 * 2 = 5.08
and continuing for other values shows that this is the correct option
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Zoe sells handmade jewelry at craft fairs. She bought a package of c charms. She used all the charms in the package to make 12 bracelets, and each bracelet had 8 charms.
Which diagram models the story?
The diagram that models the story is given as follows:
Right diagram.
The equation that models the story is given as follows:
c = 12 x 8.
How to model the story?The story is modeled applying the proportions from the units given in the context of the problem.
We have that the parameters are given as follows:
Zoe bought c charms.She made 12 bracelets.Each bracelet is composed of eight charms.Hence the total number of charms that she purchased is given as follows:
c/12 = 8.
c = 12 x 8. (which is the equation that models this situation).
c = 104.
The diagram that represents a multiplication of 12 by 8 is the diagram that is composed by a successive addition of twelve times the number 8, hence it is the right diagram.
Missing InformationThe complete problem is given by the image presented at the end of the answer.
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Use the distributive property to write an equivalent expression. Then
evaluate the expression
3(2+12)
Equivalent Expression
=
12 ÷ (4 − (6 × 2 − ((3 + 3) × 2 − 1)))
Answer:
Step-by-step explanation:
12 ÷ (4 − (6 × 2 − ((3 + 3) × 2 − 1)))
12 ÷ (4 − (12 − ((3 + 3) × 2 − 1)))
12 ÷ (4 − (12 − ((6) × 2 − 1)))
12 ÷ (4 − (12 − (12 − 1)))
12 ÷ (4 − (12 − 11)))
12 ÷ (4 − (1))
12 ÷ (4 − 1)
12÷3
4
Please help me solve this question
Answer:
Hope this helped thanks
according to the u.s. census bureau, 23.5% of people in the united states are under the age of 18. in a random sample of 250 residents of a small town in ohio, 28% of the sample was under 18. which one of the following statements is true?
The percentage of people under 18 in the sample of 250 people from Ohio is higher than the percentage of people under 18 in the United States.
This can be demonstrated mathematically using the following formula: (28/250)*100 = 11.2%. This is higher than the US percentage of 23.5%, which indicates that the sample of 250 people from Ohio had a higher proportion of people under 18 than the US population as a whole. To calculate this, we can use the formula to find the difference between the two percentages: (28% - 23.5%) = 4.5%. This means that the small town in Ohio has a higher percentage of people under 18 than the national average. Therefore, it is true that the percentage of people under 18 in the small town in Ohio is higher than the national average.
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The volume of fuel in a tank changes at a rate given by the equation:
V′(t)=4t/√(t^2+33_, t≥0. At t=√7 hours the tank holds 9.3 gallons. What is the volume of fuel in the tank after 6 hours?
Round answer to one decimal place.
The volume of fuel in the tank after 6 hours is 97.5 gallons.
To find the volume of fuel in the tank after 6 hours, we need to integrate the rate of change of the volume, given by V′(t)=4t/√(t^2+33), with respect to time from the initial time of t=√7 hours to t=6 hours.
The integral of V′(t) with respect to t is V(t)= 2/3 (t^3 + 33t) + C
We know that when t = √7 hours, the volume of fuel in the tank is 9.3 gallons. So we can use that information to find the value of the constant C.
9.3 = 2/3 (√7^3 + 33√7) + C
C = 9.3 - 2/3 (7^3/2 + 337^1/2)
C = 9.3 - 2/3 (343/2 + 337^1/2)
C = 9.3 - 2/3 (343/2 + 231)
C = 9.3 - 2/3 (574)
C = 9.3 - 382 = 5.5
Now we can substitute t = 6 into the equation for V(t) to find the volume of fuel in the tank after 6 hours.
V(6) = 2/3 (6^3 + 33*6) + 5.5
V(6) = 2/3 (216 + 198) + 5.5
V(6) = 2/3 (414) + 5.5
V(6) = 276/3 + 5.5
V(6) = 92 + 5.5 = 97.5
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(1 point) Let T be a matrix transformation from R" to R" . Determine whether or not T is one-to-one in each of the following situations: C 1. n = m A 2. n > m B. 3. n < m A. T is not a one-to-one transformation. B. T is a one-to-one transformation. C. There is not enough information to tell. (Enter "A", "B", "C"; not "A.", "B.", "C.")
The answer is:
1. n = m ........ .There is not enough information to tell.
2. n > m .........T is a one-to-one transformation.
3. n < m ......... There is not enough information to tell.
The transformation matrix is a matrix that transforms one vector into another vector. The positional vector of a point is changed to another positional vector of a new point, with the help of a transformation matrix.
he transformation matrix transforms a vector into another vector, which can be understood geometrically in a two-dimensional or three-dimensional space. The frequently used transformations are stretching, squeezing, rotation, reflection, and orthogonal projection.
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answer: x < 5 and –6x + 15 < 10
Step-by-step explanation:
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
A particle moves along a line so that its velocity is given by v(t)=-t^3+2t^2+2^-t for t>0. For what values of t is the speed of the particle increasing? The answer is (0.177,1.256) and (2.057, infinity).
For the values running between (0, 0.177) ∩ (2.057, ∝) the speed of the particle moving with velocity v(t)=-t³+2t²+2^(-t) will be increasing.
Here we are given an equation of the velocity of the particle to be
v(t)=-t³+2t²+2^(-t)
Now taking the first derivative of v(t) and equating it to 0 we get
v'(t) = -3t² + 4t - 2^(-t)log2 = 0
Using Shreedharachara's method of solving quadratic equations we get the values of t to be
1.25635 and 0.17634
Now these 2 values are the points of inflexion, hence we will now take values a little lesser and greater than these 2 values to determine the increasing points of the function
Let's consider 0.16, 0.18, and 1.3
v'(0.16) = -0.0572
v'(0.18) = 0.0109
v'(1.3) = -0.152
Hence here we see that the values of the first derivative will be negative
for (0, 0.177) ∩ (2.057, ∝)
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Glen is asked to convert 21 feet to yards he knows that 3 feet = 1 yard his work is shown explain glens error and show how to use a rate to find the correct solution
Answer:
Step-by-step explanation:
the answer if 7 yards because 21 feet divided by 3feet per yard you would get 7 yards
During the month of June 2022, the average price per gallon of gas was $4.42. During August of 2022, the average price per gallon of gas dropped to $3.75. What was the percent decrease from June of 2022 to August of 2022? Round to the nearest percent. The percent decrease from June of 2022 to August of 2022 was ___________ %
The percent decrease from June 2022 to August 2022 was 15%.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
During the month of June 2022, the average price per gallon of gas was $4.42.
During August of 2022, the average price per gallon of gas dropped to $3.75.
As per the question, the required solution would be as:
100 × (4.42 - 3.75) / 4.42
= 15.1583
Rounding to the nearest percent, we get
= 15%
Thus, the percent decrease was 15%.
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how many groups of 1/5 are in4
Answer:
20 groups
Step-by-step explanation:
There are 20 groups of 1/5 in 4 because you have to divide (4)/(1/5) so aplying the ear law you obtain 20.
John has 37 marbles for his collection. He gives 17 marbles to his friend Zach. How many marbles does he have left?
Answer:
20
I wish you good luck on your assignments.
If BAC=70, and ABC=60 and CE bisects BCD. then find BCE thanks
On solving the provided question we can say that the solution required angle bisector ∠BCE=50°.
What is angle bisector?An angle bisector or the bisector of an angle is a ray that divides an angle into two equal parts. For example, if a ray AX divides an angle of 60 degrees into two equal parts, then each measure will be equal to 30 degrees. Every angle has an angle bisector.
The sum of all the three angles of the triangle is 180°.
∠BAC=70° and ∠ABC=60°.
We know that in a triangle there are three angles and the sum of all the three angles is 180°.
∠ABC+∠BAC+∠BCE= 180°
Putting the values of the given angles we have,
60°+70°+∠BCE=180°
on adding the angles,
130°+∠BCE=180°
aking 130° to the right-hand side,
∠BCE=180°-130°
on solving we have,
∠BCE=50°
Therefore, the required angle is 50°.
The required angle ∠BCE=50°.
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On solving the provided question we can say that the solution required angle bisector ∠BCE=50°.
What is angle bisector?An angle bisector or the bisector of an angle is a ray that divides an angle into two equal parts. For example, if a ray AX divides an angle of 60 degrees into two equal parts, then each measure will be equal to 30 degrees. Every angle has an angle bisector.
The sum of all the three angles of the triangle is 180°.
∠BAC=70° and ∠ABC=60°.
We know that in a triangle there are three angles and the sum of all the three angles is 180°.
∠ABC+∠BAC+∠BCE= 180°
Putting the values of the given angles we have,
60°+70°+∠BCE=180°
on adding the angles,
130°+∠BCE=180°
aking 130° to the right-hand side,
∠BCE=180°-130°
on solving we have,
∠BCE=50°
Therefore, the required angle is 50°.
The required angle ∠BCE=50°.
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What’s the next number 3,-4,-11,-18,-25
Answer:-7
Step-by-step explanation:
3 to -4 the difference is -7
The answer is -7
The general equation for depreciation is given by y = A(1 – r)t, where y = current value,
A = original cost, r = rate of depreciation, and t = time, in years.
Using the general depreciation calculation, y = A(1 - r)^t, the car will be worth $12528.15 after 4 years.
How to calculate the car's value in four yearsY = A(1 - r)^t, is the general depreciation formula, which is used to solve the car's worth.
Description of the variables
y is the current value and where =?
Original cost was $24,000,
rate of depreciation was 15%, and
time was measured in years. = 4 years
plugging in the values
current value, y = A(1 - r)^t
current value, y = 24000 * (1 - 0.15)^4
current value, y = $12528.15
The car has been depreciated to $12528.15
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complete question
The general equation for depreciation is given by y = A(1 – r)t, where y = current value,
A = original cost, r = rate of depreciation, and t = time, in years.
The original value of a car is $24,000. It depreciates 15% annually. What is its value in 4 years?
Please need help with A) B) and C)
a) The y-intercept of the line is 25.66, which represents the predicted number of wins when yards allowed is 0.
b) The Seattle Sea hawks, the observed number of wins (10) is 4.12 less than the predicted number of wins based on the least-squares regression line.
c) It will increase the R-Sq and R-Sq(adj) and decrease the S.
What is the equation of least-squares regression and calculation for above answer?The equation of the least-squares regression line is given by:
Number of wins = 25.66 - 0.003131 * (Yards_allowed)
This equation shows the relationship between the number of wins for a team (the dependent variable) and the number of yards allowed by the team (the independent variable).
The slope of the line is -0.003131, which means that for every 1 yard increase in yards allowed, the number of wins decreases by 0.003131. The y-intercept of the line is 25.66, which represents the predicted number of wins when yards allowed is 0.
b) To calculate the residual for the Seattle Seahawks, we can use the equation of the least-squares regression line and the data for the team:
Residual = Observed value - Predicted value
Residual = 10 - (25.66 - 0.003131 * 4668)
Residual = 10 - (25.66 - 14.12)
Residual = -4.12
This means that for the Seattle Seahawks, the observed number of wins (10) is 4.12 less than the predicted number of wins based on the least-squares regression line.
c) The point representing the Carolina Panthers (5167 yards allowed, 15 wins) has a positive effect on the equation of the least-squares regression line because it is above the line.
This means that the team performed better than expected based on the number of yards allowed. Since this point is an outlier, it will increase the R-Sq and R-Sq(adj) and decrease the S.
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Evaluate the expression 1^4+3(10-2)^2show your work
Answer: 193
Step-by-step explanation:
1^4 + 3(10 - 2)^2
1^4 + 3(8)^2
1^4 + 3(64)
1^4 +192
1 + 192
193
What is the probability that a test correctly rejects a false null hypothesis called? Choose the correct answer below. A. P-value B. power of the test C. Type II error D. significance level
The correct answer is B. power of the test
The probability that a test correctly rejects a false null hypothesis is referred to as the power of the test. It is a statistical measure that helps us to determine the effectiveness of a test in detecting a real difference or effect when it exists. The power of the test is generally represented by the Greek letter beta (β) and is calculated as 1-β.
A test with a high power value is more likely to correctly reject a false null hypothesis, which means it is better at detecting the real difference or effect when it exists. On the other hand, a test with a low power is more likely to fail to reject a false null hypothesis, which means it is not as effective in detecting the real difference or effect. The p-value and significance level are also statistical measures used in hypothesis testing, but they are not directly related to the power of the test.
P-value refers to the probability of observing a test statistic as extreme or more extreme as the one observed, given that the null hypothesis is true. Significance level refers to the threshold of p-value beyond which the null hypothesis will be rejected.
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Write a function rule for "The output is three less than the input x y=
The statement "The output is three less than the input x" as an expression is y = x - 3
How to determine the function rule statement as an equationFrom the question, we have the following parameters that can be used in our computation:
A mathematical statement
The mathematical statement is given as
The output is three less than the input x
Less than here means minus
So, we have the following representation
The output is three less than the input x = x - 3
The question does not require that we solve the expression
So, we leave it at x - 3
Introduce the output varianle
y = x - 3
Hence, the required expression is y = x - 3
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help me answer a. b. c. d. e. and f
Answer:
The correct answer is F hope you have a hood day
Estimate sum of 1 1/3 and 2 3/4
Answer:
estimation: 4
real: 4 1/12
Step-by-step explanation:
Estimation: 1+2=3 1/3+3/4= around 1 3+1=4
Real= 4/3+ 11/4 = 4 1/12
The amount of water in the tank is decreasing at 600 gallons per hour.
True
False
Answer:
True.
Step-by-step explanation:
Answer:
True.
The statement "The amount of water in the tank is decreasing at 600 gallons per hour" is true. It means that the water level in the tank is going down by 600 gallons per hour, which means that the water is being used or drained out of the tank at a rate of 600 gallons per hour.
Step-by-step explanation:
1 2 3 4 5 6 7 8 9 10 A graph has quantity on the x-axis and price on the y-axis. Demand curve points are at (20, 70), (40, 40), (60, 10).A graph has quantity on the x-axis and price on the y-axis. A demand line goes through (20, 70), (40, 80), (60, 90). Based on the demand graph and the supply graph shown above, what is the price at the point of equilibrium? a. 100 b. 70 c. 40 d. There is not enough information given to determine the point of equilibrium. Please select the best answer from the choices provided A B C D Mark this and return
Answer:
B) 70
Step-by-step explanation:
Given polynomials p(x), q(x), and r(x), p(x) + ( q(x) + r(x) ) = ( p(x) + q(x) ) + r(x)
To verify the associative property of addition, begin by finding the sum of the polynomials:
(3x + 4) + ((5x2 - 1) + (2x + 6))
Associative property of addition is applied in adding the polynomials to give
5x² + 5x + 9
What is associative property of addition?According to the associative property of addition, altering how the addends are grouped has no effect on the sum.
This is applied in the addition of the given polynomial (3x + 4) + ((5x² - 1) + (2x + 6))
Addition of the polynomial
= (3x + 4) + ((5x² - 1) + (2x + 6))
= (3x + 4) + (5x² + 2x + 5)
= 5x² + 2x + 3x + 5 + 4
= 5x² + 5x + 9
altering the addends
= (5x² - 1) + ((3x + 4) + (2x + 6))
= (5x² - 1) + (3x + 4 + 2x + 6)
= 5x² - 1 + 5x + 10
= 5x² + 5x + 9
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The definition of the absolute value of a number is its magnitude, or distance, from zero. How do these two definitions connect?
The way that the definitions of the absolute value of a number, connect is that the absolute value of a number is the positive representation of the number's distance from zero.
What is absolute value ?The absolute value of a number is the numerical value of a real number without regard to its sign. In other words, the absolute value of a number is the number's distance from zero on the number line. The absolute value of a number is always positive or zero, and is written as the number inside of absolute value notation, which is two vertical lines on either side of the number, like so: |number|. For example, the absolute value of -5 is 5, and the absolute value of 5 is also 5.
The distance from zero is the same as the magnitude of a number, and the absolute value of a number is a non-negative representation of its magnitude. So, in other words, the absolute value of a number is its distance from zero on the number line. The two definitions are connected because the absolute value of a number is a positive representation of its distance from zero.
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2.1 8cm B. a 10cm D b 2.1.1 Calculate the length of a. 2.1.2 Calculate the length of b. 9cm C
need working out
Answer:
a = 6 , b = 17
Step-by-step explanation:
using Pythagoras' identity.
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
using right triangle ABD , then
a² + 8² = 10²
a² + 64 = 100 ( subtract 64 from both sides )
a² = 36 ( take square root of both sides )
a = [tex]\sqrt{36}[/tex] = 6
using right triangle ABC
note that BC = a + 9 = 6 + 9 = 15
b² = 8² + 15² = 64 + 225 = 289 ( take square root of both sides )
b = [tex]\sqrt{289}[/tex] = 17